Critical Speed

The critical speed of a tube mill is that speed of rotation at which the centrifugal power

neutralizes the force of gravity which influences the grinding balls, the grinding balls don't

fall and therefore don't perform grinding work. Or to make the definition more easy, critical

speed is the rotational speed in rpm of the mill relative to the speed at which centrifugal force

just counters gravitation and holds the charge against the shell during rotation.

Raw mills usually operate at 72-74% critical speed and cement mills at 74-76%.

Calculation of the Critical Mill Speed:

G: weight of a grinding ball in kg.

w: Angular velocity of the mill tube in radial/second. w = 2*3.14*(n/60)

Di: inside mill diameter in meter (effective mill diameter).

n: Revolution per minute in rpm

Assumed, a ball is located at the point m of the mill, the angle α represents the dynamic angle

of repose. In this case the ball is subject to the influence of two forces acting in different

direction;

1. The centrifugal power:

C = m*w*r

C = G*w2*(r/g)

G = m*g

m = G/g

2. The resulting force of gravity:

P = G.sin α

To maintain the ball in this position on the mill wall, it is necessary to satisfy the requirement

that C ≥ P or (G/g)*w2*r ≥ G.sin α

If α=90 degree then sin 90=1, when the location of the ball is in point m1, it follows that

w2*r ≥ g

(2*3.14*(n/60))2*r ≥ g

n = (3600*g/4*3.14*3.14*r)0.5 = (3600*9.81/(4*3.14*3.14*(D/2)))0.5

In this speed the grinding balls don't perform any useful w

 np=32/(Di)0.5 (Practical Speed)

For a mill to work in the optimum condition, the speed of rotation must get as close as

possible to 75% of the critical speed, and normal speeds are considered to be between 67 and

78% of the critical speed.

 %n = ((Operating speed) / nc)) * 100

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